The present invention relates generally to a computer system and method for detecting periodic and quasi-periodic signals buried in wide-band noise. Specifically, this invention relates to a computer system and method for detecting periodic and quasi-periodic signals using a novel auto power spectral density plot.
The use of an auto power spectral density (PSD) function to detect periodic and quasi-periodic signals combined with wide-band noise is well known in the art. A conventional PSD plot of a signal containing periodic signals may be created by the steps of: 1) segmenting the signal into an ensemble of equal-size, adjacent block signals, 2) calculating a Discrete Fourier Transform (DFT) of each block signal to obtain an ensemble of frequency signals containing complex data associated with frequency components, or frequency spectra, the complex data including a magnitude component and a phase component; 3) calculating a power component for each frequency component in each frequency signal using only the magnitude components from the complex data, 4) calculating an average power component for each frequency component by averaging the power components from each frequency signal, and 5) displaying the average power component for each frequency component.
Periodic signals appear as peak average power components in the PSD plot because the power associated with a periodic signal having a given frequency is concentrated around that given frequency. The average power component associated with wide-band noise, on the other hand, is spread over the entire range of frequencies in the PSD plot. Thus, a conventional PSD plot allows one to identify periodic signals based on the peak average power component in the PSD plot.
If the signal contains quasi-periodic signals, the quasi-periodic signals must be transformed into periodic signals before generation of a conventional PSD plot. Examples of signals that may include quasi-periodic signals include vibration signals obtained from rotary machines. PSD plots are typically used to analyze vibration signals in order to provide early detection of mechanical defects within the rotary machine. However, during steady state operation of a rotary machine, the shaft rotational speed tends to momentarily increase and decrease as a result of dynamic load variations on the shaft. As a result, all of the speed-related components of the vibration signal (e.g., synchronous harmonics, sub-harmonics, bearing signature, gear signature, etc.) are quasi-periodic rather than purely periodic. Those skilled in the art will recognize that generating a conventional PSD plot of a quasi-periodic signal will result in a PSD plot that contains misleading information regarding the quasi-periodic signal. Thus, quasi-periodic signals must be transformed into periodic signals before generation of a conventional PSD plot.
Several methods for transforming a digital signal containing quasi-periodic signals are known in the art. Typically, prior art methods, such as the Order Tracking method, require the use of an additional pulse tachometer type sensor signal (also known as a key-phasor signal). The key phasor signal provides a measure of the time required for the shaft to complete one revolution. Using the key-phasor signal, the original signal, which is sampled with a uniform-time interval, is re-sampled with a fixed number of samples during each shaft revolution. Linear interpolation or spline curve fitting may be used for large speed variations. Within the re-sampled signal, quasi-periodic signals become periodic signals.
Conventional PSD plots, however, may not be used to detect weak periodic and quasi-periodic signals buried in wide-band noise. That is, periodic and quasi-periodic signals associated with a frequency in the PSD plot where the average power component of the frequency is less than the average power component of the wide-band noise. As a result, some periodic signals and quasi-periodic signals that may contain valuable information may not be detected.
For example, in the context of machinery vibration analysis, periodic and quasi-periodic signals typically represent mechanical defects in rotary machines. Small amplitude periodic signals correspond to small mechanical defects and large amplitude periodic signals correspond to large mechanical defects. Small amplitude periodic signals, in turn, correspond to small average power components in conventional PSD plots. Thus, the ability to identify periodic signals having small average power components corresponds to identifying small mechanical defects.
Identification of small mechanical defects is important because repairing small mechanical defects costs less then repairing large mechanical defects. In addition, failure to identify small mechanical defects may lead to mechanical failures that cause more serious damage to the rotary machine. In some cases, the damage may be so severe that the rotary machine must be replaced. Replacement of rotary machines is a very costly proposition.
To illustrate this problem, consider a signal containing five (5) periodic signals combined with wide-band noise. The first periodic signal has an amplitude of 50 and a frequency of 500 Hz, the second, an amplitude of 10 and a frequency of 1000.50, the third, an amplitude of 5 and frequency of 1501.00, the fourth, an amplitude of 1.0 and a frequency of 2001.5, and the fifth, an amplitude of 0.5 a frequency of 2502.0. The wide-band noise is Gaussian white noise.
A conventional PSD plot (also referred to as a Raw PSD) of the signal is shown in FIG. 1. The average power component associated with the first three periodic signals may be clearly identified as the peak average power components occurring at 500, 1000, and 1500 Hz and labeled A, B, and C, respectively. The peak average power components associated with the other two periodic signals are hidden under the average power associated with the Guassian White Noise. Thus, there is a need for a method of generating a PSD plot that may be used to detect periodic and quasi-periodic signals buried in wide-band noise.
In addition, conventional PSD plots generated using Fast Fourier Transforms (FFTs) also provide an estimate of the frequency of the detected periodic signal that is limited by the FFT used to calculate the DFTs. As a result of this limitation, the estimate of frequency may be inaccurate. Referring to FIG. 1, the convention PSD plot includes an estimate of the frequencies corresponding to peaks A, B, and C. The estimated frequency is 500 Hz for peak A, 1000 Hz for peak B, and 1500 Hz for peak C. Recall that the actual frequencies should be 500 Hz, 1000.50 Hz, and 1501.00 Hz. Thus, there is a need for a method of generating a PSD plot that provides an estimate that is more accurate, that is, that more closely corresponds to the actual frequency of the detected periodic signal.
As mentioned previously, conventional PSD plots may not be used to detect periodic and quasi-periodic signals buried in wide-band noise. In addition, there are no other known computer systems and methods for detecting periodic and quasi-periodic signals buried in wide-band noise. U.S. Pat. Nos. 5,698,788, 5,686,669, 5,501,105, 4,607,529, 4,426,641, 4,408,285, and 4,352,293 teach various computer systems and methods that may be used to detect periodic and quasi-periodic signals combined with wide-band noise. However, none of these patents teach a computer system and method that may be used to generate a PSD plot that may be used to detect periodic and quasi-periodic signals buried in wide-band noise.
What is needed, then, is a computer system and method for generating a novel PSD plot that may be used for detecting periodic and quasi-periodic signals buried in wide-band noise.
Accordingly, an object of the present invention is to provide a computer system and method for detecting periodic and quasi-periodic signals buried in wide-band noise.
Another object is to provide a computer system and method for detecting periodic and quasi-periodic signals buried in wide-band noise using a novel auto power spectral density (Coherent Phase Line Enhancer (CPLE) PSD) plot.
A further object of the present invention is to provide a computer system and method for calculating an estimate of each frequency in the CPLE PSD plot.
Another object of the present invention is to provide a computer system and method for calculating a CPLE coherence plot for a CPLE PSD plot.
Still another object is to provide a computer system and method for detecting a mechanical defect in a rotary machine using the CPLE PSD plot.
These and other objects are provided, according to the present invention, by a computer system containing a software program that causes the computer system to generate and display a CPLE PSD plot for a signal containing periodic and quasi-periodic signals buried in wide-band noise.
For signals containing quasi-periodic signals, the software program causes the computer system to transform the quasi-periodic signals into periodic signals (also referred to as discretization of the quasi-periodic signals) using Order Tracking (OT) or a Phase Synchronized Enhancement Method (PSEM).
After this transformation and, for signals containing only periodic signals, the software program causes the computer system to segment the signal into an ensemble of equal size, adjacent block signals (with or without overlapping), perform a DFT on each block signal to obtain an ensemble of frequency signals, each frequency signal containing complex data associated with frequency components, define a complex frequency-time signal for each frequency component using the complex data, perform a second DFT on each complex frequency-time signal to obtain an equivalent wave number signal for each frequency component, identify a peak magnitude component for each equivalent wave number signal associated with each frequency component, define a window around each peak magnitude component, calculate the power contained within each window for each frequency component, and display the window power for each frequency component to form the CPLE PSD plot.
The software program further causes the computer system to calculate an estimate of the frequency associated with and a CPLE coherence plot for detected periodic and quasi-periodic signals. The CPLE coherence plot is basically a measure of the discreteness of each frequency component.
In a first embodiment, the present invention is used to detect mechanical failures in rotary machines by identifying periodic, or quasi-periodic, signals in vibration signals containing wide-band noise obtained from the rotary machines. Periodic signals buried in wide-band noise do not appear as peaks in conventional PSD plots and, as a result, cannot be detected using conventional PSD plots. In this first embodiment, the present invention generates a CPLE PSD plot wherein periodic signals buried in wide-band noise appear as peaks and can be readily identified.